Physics 2025 Minilab 5 Analog Circuits Digital Circuits

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Purpose of This Minilab • Gain some basic experience in reading and building electronic circuits. • Learn how digital circuits and digital logic work. • Learn some basic digital to analog interfacing.

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Analog Circuits – The Voltage Divider Suppose you have a fixed voltage power supply (Vin). To generate a voltage Vout (between 0 and Vin): Build a “voltage divider” using two resistors (R 1 and R 2). Vin R 1 Vout R 2 Ground (0 V)

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits The Voltage Divider – How it Works The total resistance of the circuit is: Rtotal = R 1+R 2 The current from Vin to ground is: Vin I Ohm’s law for R 2: R 1 Combining (2) and (3): Vout R 2 Ground (0 V) (1)

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits The Voltage Divider – How to Choose R 1 and R 2 Example task: Vin = 5 V ………. . create Vout = 2 V Vin I R 1 Vout R 2 Ground (0 V) Many Possible Solutions: R 1 = 3 W R 2 = 2 W R 1 = 30 W R 2 = 20 W R 1 = 300 W R 2 = 200 W R 1 = 3000 W R 2 = 2000 W etc.

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits The Voltage Divider – Which Solution to Choose? Many Possible Solutions: R 1 = 3 W R 2 = 2 W R 1 = 30 W R 2 = 20 W R 1 = 300 W R 2 = 200 W ……………. R 1 = 300 K W R 2 = 200 K W etc. Current I is very large (maybe too large for the power supply to handle) Current I is very small (Problem when attaching circuits with smaller resistances to Vout).

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Attaching a Simple Circuit to Voltage Divider Choose R 1 and R 2 such that: R 1<<R 3 R 2<<R 3 Otherwise Vout drops much lower and is no longer what you designed it to be. Vin R 1 R 2 Vout R 3 attached circuit For Activity 1 you should choose R 1 and R 2 to be less than 10 k. W but not too low. Recommended range: a few hundred W.

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Voltage Divider on the Bread Board To 5 V (Vin) To Ground (0 V) R 1 Vout R 2

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Measuring Vout of Voltage Divider Black clip should be on ground. For correct polarity make sure GND indicator goes into “COM” input on DMM.

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Inverting Amplifier Circuit – How it Works R 4 I I V- Vin Negative feedback loop R 3 V+ + Vout Virtual equality: Voltage at “-” input = Voltage at “+” input (V- = 0 Volt because V+ = 0 Volt) Current flows around op-amp (and basically none into it, because op-amp has very high input resistance) Current through R 3 = Current through R 4

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Inverting Amplifier Circuit – How it Works R 4 I Vin I V- R 3 V+ Applying Ohm’s Law on R 3 : Applying Ohm’s Law on R 4: + Vout

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Inverting Amplifier Circuit – How it Works R 4 I Vin I V- R 3 V+ - Vout + Example: R 4 = 10 k. W R 3 = 5 k. W Gain = - 2 This means: If Vin = 2 V then Vout = – 4 V Notice how EASY it is to design an amplifier with a specific gain simply by choosing the proper ratio of R 4 and R 3 !!!

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Inverting Amplifier Circuit – Amplifying a Signal (just to show you more applications…) R 4 Vin I I V- R 3 V+ Sinusoidal input signal + Vout Sinusoidal output signal: • Is inverted • Has different amplitude

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits The Inverting Amplifier Circuit YOU Will Build 5 V R 1 R 4 Vin - R 2 R 3 + Note: +12 V and -12 V connections for amplifier not shown in diagram. Vout Gain of amplifier circuit: Voltage divider from Activity 1 Note: Vin is now the input voltage of the amplifier circuit (don’t confuse this with prior Vin from voltage divider).

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Amplifier is an Integrated Circuit (IC): LF 351 1 + 2 3 -12 V 4 Notice the semicircular cutout (helps to identify pin number) pin 1 8 + 7 6 +12 V 8 pins (connections) 4 on each side Out 5 pin chart for LF 351 (view from top) (pins 1, 5, 8 are not used) All pin diagrams are shown in the lab manual.

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Connecting LF 351 to Create Amplifier Circuit R 4 +12 V 5 V R 1 R 3 1 8 2 7 3 6 4 5 R 2 -12 V Vout

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Using the Breadboard for IC connection 5 holes in a “column” are electrically connected. But: Red and Green are NOT connected across the center break. The center break

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Inserting IC into Bread Board Insert IC into bread board across the center divide: 4 pins on each side. Push IC all the way down. indentation pin 1 Example: Use any of these 4 holes to connect to pin 4

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits 5 6 Out 4 -12 V 3 + + 7 2 - 1 - 8 +12 V Connecting +12 V and – 12 V Power to the IC

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Complete Amplifier Circuit Voltage divider R 4 R 3 Clips attached as shown measure Vin of amplifier circuit.

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Measuring Vout of Amplifier Circuit The output voltage of the amplifier circuit is measured where R 4 attaches to pin 6 of the LF 351 IC.

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Taking out an IC Grab the IC with the yellow IC removal tool. Pull evenly and straight upwards. The IC removal tool helps to avoid bent or broken pins.

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Binary Numbers In digital electronics information is coded as binary numbers which contain only Ones and Zeroes. Example: 1001 (binary) = 1 x 23+0 x 22+0 x 21+1 x 20 = 9 (decimal) Any decimal number can be converted to a binary number and stored electronically (e. g. , in a computer). 1’s and 0’s are often stored as High (5 Volt) and Low (0 Volt) voltages. For example, the number shown above (1001) could be represented by 4 “data lines” that have either high or low voltages. 1 0 5 V 0 V 0 1 0 V 5 V

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits – The Basic Idea Input #1 Digital Circuit Output Input #2 Digital circuits have one or more “inputs” and one or more “outputs”. • Inputs are wires or pins to which a given voltage is applied. • Outputs are wires or pins that provide a certain voltage. The value of the output voltage depends on the value of the voltages applied to the inputs. Never apply a voltage to an output! The output already generates its own voltage. You can “read” that voltage (e. g. , with a DMM).

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits – The Basic Idea Input #1 Digital Circuit Output Input #2 Why are they called “digital”? Because we apply only two specific voltages to the inputs and we can only receive one of these two voltages on the output, nothing else. These two voltages are called “High” and “Low” voltage. They are also called “ 1” and “ 0” They can represent a binary number (“digit”). Digital circuits are some of the basic building blocks in computers.

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits – TTL Input #1 Digital Circuit Output Input #2 “TTL” (Transistor-Transistor Logic) circuits are digital circuits that use the following “High” and “Low” voltages: High = 5 Volts = “ 1” Low = 0 Volts = “ 0”

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits – Example: The Inverter Input Inverter Output Inverter has only one input and one output. How the inverter behaves: If you apply a “high” voltage to the input You get “low” voltage at the output. If you apply a “low” voltage to the input You get “high” voltage at the output. …in other words … 5 V on input 0 V on output 0 V on input 5 V on output …in other words … “ 1” on input ” 0” on output “ 0” on input “ 1” on output

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits – The Inverter The official symbol This ring symbolizes “inverting”. Truth Table for Inverter Input 0 1 Output 1 0

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits The “AND” Gate – Another Digital Circuit A Q B Truth Table for AND Gate Input A Input B Output Q = A • B 0 1 0 0 1 1 0 0 0 1

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits The “NAND” Gate – Another Digital Circuit Indicates “invert” A Q B Truth Table for NAND Gate Input A Input B Output Q = A • B 0 1 0 0 0 1 1 0 Just like “AND” gate but additionally inverted”.

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits What Good are Digital Circuits? Digital circuits are basically automated decision makers. Very simple example: A burglar alarm that rings a bell when a door is open but only when the alarm is actually activated. You can use an “AND” gate. Circuit that produces 5 V signal if door is open and 0 V when closed. Circuit that produces 5 V when alarm is “ON”, 0 V when it is “OFF”. Circuit that rings a bell when 5 V is applied. By combining digital circuits you can build very complicated decision making machines.

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits 4081 : The AND Gate IC (contains 4 gates) 5 Volt View from the top Input A Input B A and B could, for example, be connected to SW 1 and 2 on the bread board. Output Q could, for example, be connected to the logic indicator (green LED) on the bread board.

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Digital to Analog Converter (DAC) The music on an I-pod or on a CD is stored digitally as lots of binary numbers. To actually create sound when playing the music these binary numbers (digital) must be converted into “analog” voltages (the garden-variety that is not limited to specific “High” and “Low” voltages). Once those analog voltages are generated from the digital data they can then be applied to a loudspeaker. Speaker CD (digital data) DAC

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Building a Basic DAC With an Op-Amp I 1 Switches (5 V or 0 V) SW 1 SW 2 SW 3 SW 4 5. 6 k. W I 2 10 k. W I 3 R 4 I I V 0 Volt + 22 k. W I 4 V+ 47 k. W We know this voltage (virtual equality) Vout More current means higher Vout.

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits SW 1 SW 2 SW 3 SW 4 I 1 5. 6 k. W I 2 10 k. W I 3 R 4 I I V 0 Volt 22 k. W I 4 V+ - Vout + 47 k. W If SW 1 is “ 0” I 1=0 If SW 1 is “ 1” (5 V) I 1=5 V/5. 6 k. W Similar for I 2, I 3, I 4

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits SW 1 SW 2 SW 3 SW 4 I 1 5. 6 k. W I 2 10 k. W I 3 R 4 I I V 0 Volt 22 k. W I 4 V+ + Vout 47 k. W With SW 1…. SW 4 you can switch on and off I 1…. . I 4. I will become more or less. Vout will become more or less.

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits SW 1 SW 2 SW 3 SW 4 I 1 5. 6 k. W I 2 10 k. W I 3 22 k. W I 4 R 4 I I V 0 Volt V+ + Vout 47 k. W Because the 4 resistances are different, the 4 currents (when switched on) will be different. When SW 1 is switched on more current is added than when SW 2 or SW 3 or SW 4 is switched on. SW 1 has a greater influence on Vout than SW 2 (contributes more to I). SW 2 has a greater influence on Vout than SW 3. Etc. .

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits SW 1 SW 2 SW 3 SW 4 I 1 5. 6 k. W I 2 R 4 I 10 k. W I 3 22 k. W I 4 I V 0 Volt V+ + Vout 47 k. W The 4 resistances are weighted differently by factors of about 2, 4, and 8 just like digits in binary numbers. If the 4 inputs represent a 4 digit binary number, the output voltage is proportional to the value represented by that binary number. Build the circuit and try it out!

Physics 2025 Minilab 5: Analog Circuits / Digital Circuits Remember: These power point presentations are available on our website, so you can download them on the computer at your lab table.